STATISTICAL PROPERTIES OF THE ARITHMETIC CORRELATION OF SEQUENCES

In this paper we study arithmetic correlations of sequences. Arithmetic correlations are the with-carry analogs of classical correlations. We analyze the arithmetic autocorrelations of non-binary ℓ-sequences, showing that they are nearly optimal. We analyze the expected auto- and cross-correlations...

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Bibliographic Details
Published in:International journal of foundations of computer science 2011-09, Vol.22 (6), p.1297-1315
Main Authors: GORESKY, MARK, KLAPPER, ANDREW
Format: Article
Language:English
Subjects:
Analogs
Arithmetic
Autocorrelation
Correlation
Correlation analysis
Foundations
Optimization
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Summary:In this paper we study arithmetic correlations of sequences. Arithmetic correlations are the with-carry analogs of classical correlations. We analyze the arithmetic autocorrelations of non-binary ℓ-sequences, showing that they are nearly optimal. We analyze the expected auto- and cross-correlations of sequences with fixed shift, averaged over all sequences with a fixed period. We analyze the expected autocorrelations of a fixed sequence, averaged over all shifts.
ISSN:0129-0541
1793-6373
DOI:10.1142/S0129054111008726